limlne^(lnx+1/x)=limln(xe^(1/x))=ln[lime^(1/x)/(1/x)]=ln[lim-1/x²e^(1/x)/(-1/x²)]=ln[lime^(1/x)]=limln[e^(1/x)]=lim1/x=+∞通分这个lim[lnx+(1/x)] = lim[(xlnx+1)/x]分母x→0+,分子lim(xlnx+1) = ...